**Contemporary Mathematics**

Volume: 267;
2000;
356 pp;
Softcover

MSC: Primary 16;

Print ISBN: 978-0-8218-2126-8

Product Code: CONM/267

List Price: $92.00

Individual Member Price: $73.60

**Electronic ISBN: 978-0-8218-7857-6
Product Code: CONM/267.E**

List Price: $92.00

Individual Member Price: $73.60

# New Trends in Hopf Algebra Theory

Share this page *Edited by *
*Nicolás Andruskiewitsch; Walter Ricardo Ferrer Santos; Hans-Jürgen Schneider*

This volume presents the proceedings from the Colloquium on Quantum Groups and Hopf Algebras held in Córdoba (Argentina) in 1999. The meeting brought together researchers who discussed recent developments in Hopf algebras, one of the most important being the influence of quantum groups.

Articles offer introductory expositions and surveys on topics of current interest that, to date, have not been available in the current literature. Surveys are included on characteristics of Hopf algebras and their generalizations, biFrobenius algebras, braided Hopf algebras, inner actions and Galois theory, face algebras, and infinitesimal Hopf algebras. The following topics are also covered: existence of integrals, classification of semisimple and pointed Hopf algebras, \(*\)-Hopf algebras, dendriform algebras, etc. Non-classical topics are also included, reflecting its applications both inside and outside the theory.

#### Table of Contents

# Table of Contents

## New Trends in Hopf Algebra Theory

- Contents vii8 free
- Preface ix10 free
- Participants xi12 free
- Program xiii14 free
- Infinitesimal Hopf algebras 118 free
- Modules over weak entwining structures 3148
- On generalized characters 5572
- BiFrobenius algebras 6784
- Integrable models and star structures 99116
- On Nichols algebras of low dimension 111128
- A generalization of crossed products 135152
- A brief introduction to face algebras 161178
- On two proofs for the existence and uniqueness of integrals for finite-dimensional Hopf algebras 177194
- Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension 195212
- Pointed indecomposable Hopf algebras over Coxeter groups 215232
- A duality theorem for quantum groupoids 237254
- Primitive elements in a free dendriform algebra 245262
- On operator representations of Uq(isl(2, JR)) 265282
- Duals and doubles of quantum groupoids (X R-Hopf algebras) 273290
- Survey of braided Hopf algebras 301318
- Inner and outer actions of pointed Hopf algebras 325342
- Quasi-triangular structures on Hopf algebras with positive bases 339356

#### Readership

Graduate students and research mathematicians interested in Hopf algebras and quantum groups; algebraists; specialists in combinatorics; mathematical physicists.